In semiconductor manufacturing, groups or “batches” of wafers are manufactured through a series of processes. Typically, a number of measurements are observed at one or more of the processes to assess performance. Examples of such measurements include wafer temperature, wafer thickness, and the like. These measurements can then be provided to a control model to provide a statistical characterization for the state of each process. This characterization of data, however, is lacking for several reasons. One reason is that that time intervals between the processes are not uniform. Another reason is that the total duration of the process for each batch of wafers can be different. Yet another reason is that collected time registrations are not synchronized to one another and common events are not aligned. Another reason is that some measurements are not included in the data collection. As a result, limits of the control model have to be broadly defined, which leads to potential faults that would otherwise be detected.
Typically, control models use statistical analysis to accommodate these potential faults. One statistical analysis device utilizes a calculated average of readings across time samples for processing steps of each batch. This device, however, fails to show dynamic variations with respect to time, because only an average value of each processing step of wafer batches is calculated. For example, the average values across several wafers or several batches may remain very close even though the variable profiles behave very differently with respect to time. In addition, due to unsynchronized projected trajectories of the control models, the anticipated data pattern may not be reached and misleading conclusions may be drawn as a result.
Furthermore, if measurements are missing from the control model, the missing measurements are assumed to be insignificant for the collected data. For example, if a measurement is missing from a data collection, an average based on the remaining measurements is calculated instead of an average based on the entire measurement. This may result in an output that does not provide a correct statistical characterization of the data.
Moreover, current control models are insensitive to spikes or other abrupt changes, such as a dramatic drop of values, that need extra attentions. This may also result in an output that does not provide a correct statistical characterization of the data.
Therefore, a need exists for a control model and method that screens or filters the collected data in such a way that synchronizes wafer-to-wafer and/or batch-to-batch maturity, equalizes wafer process durations, handles missing data, and adjusts incidental anomalies.